This sounds like classic "black spot" disease. It is very common with
roses. Pruning off some of the top part to allow sun and air into
the plant helps. To prevent black spot, I use Ortho Rose Fungicide
every ten days (in a garden sprayer) from early spring until summer,
then once every two weeks. I have not seen black spot since 1998
(when I did not use the fungicide.) After black spot takes hold, it
is difficult to control. All you can do now is prune out some canes
and burn what is removed to prevent it from coming back next year.
I've tried a more environmental-friendly method using a baking soda
solution spray, but it did not work too well and the baking soda left
a white film on the leaves.